— Alan Greenspan
Misattributed, Attributed to Greenspan by Rupert Cornwell, "Alan Greenspan: The buck starts here" http://www.independent.co.uk/news/people/profiles/alan-greenspan-the-buck-starts-here-595789.html, The Independent, 27 April 2003, citing an unspecified Capitol Hill hearing. However, as Ralph Keyes notes in The Quote Verifier (2006, p. 233), "This popular tongue twister gets attributed to the obfuscator du jour." The earliest known print attribution is to Robert McCloskey, U.S. State Department spokesman, by Marvin Kalb, CBS reporter, in TV Guide, 31 March 1984, citing an unspecified press briefing during the Vietnam war.
Earlier attributions include: "a high government official", Annual Report, North American Gas Tax Conference, Federation of Tax Administrators, 1967; Jerry Lewis (a sign pasted on the camera during a movie shoot), by Dick Kleiner, Hollywood Correspondent, Sumter Daily Item, Feb. 4, 1970; a sign on the desk of Suzanne Schroeder, collector of bureaucratic gobbledygook, AP wire story, Sarasota Herald-Tribune, July 3, 1973; Jack Nicklaus paraphrasing Richard Nixon, by Larry Dorman, The Palm Beach Post, Dec. 8, 1979; and "a Hollywood film director", by J.D. Douglas, The Third Way, 29 December 1977. Additionally, a thesis monograph by Michael David Katz, Georgia State University, 1973 is titled with the quote.
On the back of the first Stealers Wheel album, a very similar statement attributed to band member Rod Coombes is found: "We know that you believe you understand what you think we said, but we are not sure you realize that what you heard is not what we meant." The album was released in 1972.
See Richard Nixon: "Now, when individuals read the entire transcript of the [March] 21st  meeting, or hear the entire tape, where we discussed all these options, they may reach different interpretations, but I know what I meant, and I know also what I did"